TECHNICAL NOTE—Robust Newsvendor Competition Under Asymmetric Information

We generalize analysis of competition among newsvendors to a setting in which competitors possess asymmetric information about future demand realizations, and this information is limited to knowledge of the support of demand distribution. In such a setting, traditional expectation-based optimization criteria are not adequate, and therefore we focus on the alternative criterion used in the robust optimization literature: the absolute regret minimization. We show existence and derive closed-form expressions for the robust optimization Nash equilibrium solution for a game with an arbitrary number of players. This solution allows us to gain insight into the nature of robust asymmetric newsvendor competition. We show that the competitive solution in the presence of information asymmetry is an intuitive extension of the robust solution for the monopolistic newsvendor problem, which allows us to distill the impact of both competition and information asymmetry. In addition, we show that, contrary to the intuition, a competing newsvendor does not necessarily benefit from having better information about its own demand distribution than its competitor has

Quantifying the efficiency of price-only contracts in push supply chains over demand distributions of known supports

In this paper, we quantify the efficiency of price-only contracts in supply chains with demand distributions by imposing prior knowledge only on the support, namely, those distributions with support [a, b] for 0 < a <_ b < +1. By characterizing the price of anarchy (PoA) under various push supply chain configurations, we enrich the application scope of the PoA concept in supply chain contracts along with complementary managerial insights. One of our major findings is that our quantitative analysis can identify scenarios where the price-only contract actually maintains its efficiency, namely, when the demand uncertainty, measured by the relative range b/a, is relatively low, entailing the price-only contract to be more attractive in this regard

Robust newsvendor problem with autoregressive demand

This paper explores the classic single-item newsvendor problem under a novel setting which combines temporal dependence and tractable robust optimization. First, the demand is modeled as a time series which follows an autoregressive process AR(p), p ≥ 1. Second, a robust approach to maximize the worst-case revenue is proposed: a robust distribution-free autoregressive forecasting method, which copes with non-stationary time series, is formulated. A closed-form expression for the optimal solution is found for the problem for p = 1; for the remaining values of p, the problem is expressed as a nonlinear convex optimization program, to be solved numerically. The optimal solution under the robust method is compared with those obtained under two versions of the classic approach, in which either the demand distribution is unknown, and assumed to have no autocorrelation, or it is assumed to follow an AR(p) process with normal error terms. Numerical experiments show that our proposal usually outperforms the previous benchmarks, not only with regard to robustness, but also in terms of the average revenue.Ministerio de Economía y CompetitividadJunta de Andalucí

Four Contributions to Experimental Economics

In the following four chapters, distinct but related experimental research analyzing strategic and non-strategic economic behavior is presented. Chapter 2, entitled "Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games" is a systematic study of behavior in symmetric and asymmetric prisoner's dilemma games. The prisoner's dilemma is one of the key models in many disciplines for now over five decades. Previous prisoner's dilemma experiments show that in contrast to theoretical predictions, cooperation rates are generally very high in the symmetric payoff variant of the game. Chapter 2 studies cooperation in the prisoner's dilemma in a more realistic scenario by systematically analyzing the effects of asymmetric payoffs. Already in the early nineties Murnighan et al. (1990) noted that "research has been inexplicably absent on the effects of asymmetry". The present study takes this concern into account and focuses on this much broader type of conflict expanding the limited and rather unsystematic research conducted in this area. It analyzes and discusses the effect of asymmetry on cooperation in a 40 period prisoner's dilemma game in fixed partner design. A distinction is made between a high and low payoff symmetric prisoner's dilemma on the one hand and an asymmetric game combined out of both symmetric ones on the other hand. Asymmetry significantly decreases cooperation, as low-type players are more likely to defect after mutual cooperation while high-type players initiate cooperation more often than the former. Asymmetry also has a significant negative effect on the stability of cooperation rendering long sequences of mutual cooperation extremely rare. These results are not only a valuable addition to the existing (mostly symmetric) prisoner's dilemma literature but are also of relevance for understanding reciprocity, equity and fairness especially in light of recent theoretical developments based exclusively on symmetric experimental games. Chapter 3, entitled "Assignment versus Choice in Prisoner's Dilemma Experiments'' compares behavior in a repeated prisoner's dilemma game when players can choose between two different representations of the same prisoner's dilemma, to behavior when players are assigned to play a specific game. The chapter is concerned with the methodological question of the external validity of experimental research based on the assignment of participants to experimental games or decision situations. Experimental findings may systematically misrepresent field outcomes if assigning participants to experiments has an impact on the decisions made by the participants in the experiment and if such an assignment does not occur in the field. The chapter therefore analyzes to what extent experimental deviations from actual situations due to the assignment of participants is based exclusively on the possibility of self-selection or sorting, or whether choice has an important behavioral effect in itself. The chapter extends the results obtained in the experimental psychology literature by analyzing whether choice effects are also found in strategic contexts, rendering them of particular interest to economic environments. Based on the idea that choice either via active modification of the strategic environment or by passive self-selection into a particular strategic environment may be an important property of many empirical problems studied using experimental methods, the research goal is to separate a choice effect from sorting or self-selection effects. The experimental results clearly indicate that the mere fact that participants can choose the game they want to play has a statistically significant impact on behavior. Cooperation rates are up to 60% higher in the games that were not assigned to but chosen by participants. These findings are consistent with the robust evidence of the psychology literature on non-strategic contexts that choice increases motivation, trust, and performance. Given that in many contexts agents choose the strategic situation they get involved in, assigning participants to experiments may affect the external validity of some experimental findings. Chapter 4, entitled "The Role of Rivalry - Public Goods versus Common-Pool Resources" moves from the 2 person prisoner's dilemma game structure to the analysis of behavior in a 4 person quadratic public good and a quadratic common-pool resource game. Despite a large theoretical and empirical literature on public goods and common-pool resources, a systematic comparison of these two types of social dilemmas is lacking. In fact, there is some confusion about these two types of dilemma situations. As a result, they are often treated alike. An explicit example of this is provided by Gintis (2000) who argues that while "common pool resource and public goods games are equivalent for Homo Oeconomicus, people treat them quite differently in practice. This is because the status quo in the public goods game is the individual keeping all the money in the private account, while the status quo in the common pool resource game is that the resource is not being used at all." In line with the theoretical literature, the chapter first establishes theoretically that public good and common-pool resource games as used in the experimental literature are two distinct types of social dilemmas, the fundamental difference between the two games being the degree of rivalry. It is shown that the distinguishing feature of these two types of games lies in the distributional factor that determines whether the good is rival or non-rival. This difference gives rise to two distinct strategic environments. Based on these theoretical differences an experiment is devised that tests whether the theoretical differences have an impact on behavior. The results show that participants clearly respond to the differences in rivalry. Aggregate behavior in both games starts relatively close to Pareto efficiency and converges quickly to the respective Nash equilibrium. This clearly indicates that the differences in rivalry affect behavior, strengthening the importance of differentiating between the two types of games. Despite this difference reflecting the structure of the two games, there appear to be some behavioral similarities. In both games, aggregate behavior starts in the neighborhood of the Pareto optimum and moves rather quickly to the respective aggregate Nash equilibrium. Chapter 5 entitled "Purchase Decisions with Non-linear Pricing Options under Risk" moves away from a strategic game setting to an analysis of decisions under risk. The chapter reports on an experimental investigation of purchase decisions with linear and non-linear pricing under risk. Standard economic theory suggests that customers should be indifferent to the format of a price reduction. In particular this implies that one would expect a customer to switch from one pricing scheme to another (one supplier to another) as long as there is at least an expected reduction in the effective purchase price. The recent surge in the use of rebates, discounts, bonus and point schemes implemented by retailers but also observed in other levels of the production chain begs the question of whether traditional economic explanations do fully account for the increased usage of non-linear pricing methods. An understanding of potential behavioral reasons for using such pricing schemes - as presented in this chapter - may not only be relevant for their design, but also for wider policy considerations. The experiment presented is based on a single period stochastic inventory problem with endogenous cost. It extends classic binary lottery experiments to test standard decision theoretic predictions concerning purchasing behavior in a rebate and a discount scheme. The question to what extent customers continue to purchase under two mathematically isomorph formats of non-linear schemes even if switching to a linear pricing scheme is optimal is investigated. The results indicate that rebate and discount schemes exert a statistically significant attraction on customers. Given the increased role of non-linear pricing schemes, systematic deviations from optimal behavior are an important element in the design of such schemes and may raise consumer protection and competition policy issues. The chapter concludes with a discussion on how the results can be explained by decision heuristics.</p

Three essays on product management : how to offer the right products at the right time and in the right quantity

Across virtually all industries, firms share one common objective: they strive to match their supply with customer demand. To achieve this goal, firms need to offer the right products at the right time and in the right quantity. Only firms that excel in all three dimensions can provide products with a high customer value and achieve extraordinary profits. This thesis investigates specific challenges that a firm has to overcome on its way to a good match between supply and demand. The first essay investigates how a firm can already select the right products during the product development phase. To make good resource allocation decisions, the firm needs to collect valuable information, and incentivize information sharing across the entire organization. The key result is that the firm needs to balance individual and shared incentives to achieve this goal. However, such compensation schemes come at the cost of overly broad product portfolios. The second essay examines how uncertain customer demand patterns affect seasonal products. Specifically, the timing of the product’s availability is crucial. Too early, and high opportunity and inventory costs may devour profits. Too late, and the firm loses its customers. In short, the firm has to balance a product’s market potential with the costly market time. This tradeoff may induce a firm to stock more inventories to satisfy a smaller market potential. Lastly, the third essay investigates how customer substitution influences the inventory decisions of different supply chain members in the presence of upstream competition. We find that customer substitution has a non-monotonic effect on the supply chain members’ decisions, and that left-over inventories may decline even when initial inventories are raised

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

This paper studies government subsidies for green technology adoption while considering the manufacturing industry’s response. Government subsidies offered directly to consumers impact the supplier’s production and pricing decisions. Our analysis expands the current understanding of the price-setting newsvendor model, incorporating the external influence from the government, who is now an additional player in the system. We quantify how demand uncertainty impacts the various players (government, industry, and consumers) when designing policies. We further show that, for convex demand functions, an increase in demand uncertainty leads to higher production quantities and lower prices, resulting in lower profits for the supplier. With this in mind, one could expect consumer surplus to increase with uncertainty. In fact, we show that this is not always the case and that the uncertainty impact on consumer surplus depends on the trade-off between lower prices and the possibility of underserving customers with high valuations. We also show that when policy makers such as governments ignore demand uncertainty when designing consumer subsidies, they can significantly miss the desired adoption target level. From a coordination perspective, we demonstrate that the decentralized decisions are also optimal for a central planner managing jointly the supplier and the government. As a result, subsidies provide a coordination mechanism

Closed-Form Solutions for Distributionally Robust Inventory Management: Extended Reformulation using Zero-Sum Game

When only the moments (mean, variance or t-th moment) of the underline distribution are known, numerous max-min optimization models can be interpreted as a zero-sum game, in which the decision maker (DM) chooses actions to maximize her expected profit while Adverse Nature chooses a distribution subject to the moments conditions to minimize DM’s expected profit. We propose a new method to efficiently solve this class of zero-sum games under moment conditions. By applying the min-max inequality, our method reformulates the zero-sum game as a robust moral hazard model, in which Adverse Nature chooses both the distribution and actions to minimize DM’s expected profit subject to incentive compatibility (IC) constraints. Under quasi-concavity, these IC constraints are replaced by the first-order conditions, which give rise to extra moment constraints. Interestingly, these extra moment constraints drastically reduce the number of corner points to be considered in the corresponding semi-infinite programming models. We show that in the equilibrium, these moment constraints are binding but have zero Lagrangian multipliers and thus facilitate closed-form solutions in several application examples with different levels of complexity. The high efficiency of the method enables us to solve a large class of zero-sum games and the corresponding max-min robust optimization models

A New Method to Solve Zero-Sum Games under Moment Conditions

When only the moments (mean, variance or t-th moment) of the underline distribution are known, numerous max-min optimization models can be interpreted as a zero-sum game, in which the decision maker (DM) chooses actions to maximize her expected profit while Adverse Nature chooses a distribution subject to the moments conditions to minimize DM’s expected profit. We propose a new method to efficiently solve this class of zero-sum games under moment conditions. By applying the min-max inequality, our method reformulates the zero-sum game as a robust moral hazard model, in which Adverse Nature chooses both the distribution and actions to minimize DM’s expected profit subject to incentive compatibility (IC) constraints. Under quasi-concavity, these IC constraints are replaced by the first-order conditions, which give rise to extra moment constraints. Interestingly, these extra moment constraints drastically reduce the number of corner points to be considered in the corresponding semi-infinite programming models. We show that in the equilibrium, these moment constraints are binding but have zero Lagrangian multipliers and thus facilitate closed-form solutions in several application examples with different levels of complexity. The high efficiency of the method enables us to solve a large class of zero-sum games and the corresponding max-min robust optimization models